The positioning of a moving platform, such as, wheel-based platforms/vehicles or individuals, is commonly achieved using known reference-based systems, such as the Global Navigation Satellite Systems (GNSS). The GNSS comprises a group of satellites that transmit encoded signals and receivers on the ground, by means of trilateration techniques, can calculate their position using the travel time of the satellites' signals and information about the satellites' current location.
Currently, the most popular form of GNSS for obtaining absolute position measurements is the global positioning system (GPS), which is capable of providing accurate position and velocity information provided that there is sufficient satellite coverage. However, where the satellite signal becomes disrupted or blocked such as, for example, in urban settings, tunnels and other GNSS-degraded or GNSS-denied environments, a degradation or interruption or “gap” in the GPS positioning information can result.
In order to achieve more accurate, consistent and uninterrupted positioning information, GNSS information may be augmented with additional positioning information obtained from complementary positioning systems. Such systems may be self-contained and/or “non-reference based” systems within the platform, and thus need not depend upon external sources of information that can become interrupted or blocked.
One such “non-reference based” or relative positioning system is the inertial navigation system (INS). Inertial sensors are self-contained sensors within the platform that use gyroscopes to measure the platform's rate of rotation/angle, and accelerometers to measure the platform's specific force (from which acceleration is obtained). Using initial estimates of position, velocity and orientation angles of the moving platform as a starting point, the INS readings can subsequently be integrated over time and used to determine the current position, velocity and orientation angles of the platform. Typically, measurements are integrated once for gyroscopes to yield orientation angles and twice for accelerometers to yield position of the platform incorporating the orientation angles. Thus, the measurements of gyroscopes will undergo a triple integration operation during the process of yielding position. Inertial sensors alone, however, are unsuitable for accurate positioning because the required integration operations of data results in positioning solutions that drift with time, thereby leading to an unbounded accumulation of errors.
Another known complementary “non-reference based” system is a system for measuring speed/velocity information such as, for example, odometric information from a odometer within the platform. Odometric data can be extracted using sensors that measure the rotation of the wheel axes and/or steer axes of the platform. Wheel rotation information can then be translated into linear displacement, thereby providing wheel and platform speeds, resulting in an inexpensive means of obtaining speed with relatively high sampling rates. Where initial position and orientation estimates are available, the odometric data are integrated thereto in the form of incremental motion information over time.
Odometry has short-term accuracy, however, odometric data can contain errors such as those that may arise from wheel slippage. If odometry is to be used alone to obtain a positioning solution (i.e. using it to get both translational speed of the platform as well as rotational motion), the integration of motion information including errors such as wheel slippage will result in the small errors increasing without bound over time because of integration operations. For instance, it is known that orientation errors can create large positional errors that increase with the distance traveled by the platform.
Given that each positioning technique described above (INS/GNSS/Speed Information) may suffer loss of information or errors in data, common practice involves integrating the information/data obtained from the GNSS with that of the complementary system(s). For instance, to achieve a better positioning solution, INS and GPS data may be integrated because they have complementary characteristics. INS readings are accurate in the short-term, but their errors increase without bounds in the long-term due to inherent sensor errors. GNSS readings are not as accurate as INS in the short-term, but GNSS accuracy does not decrease with time, thereby providing long-term accuracy. Also, GNSS may suffer from outages due to signal blockage, multipath effects, interference or jamming, while INS is immune to these effects.
Although available, integrated INS/GNSS is not often used commercially for low cost applications because of the relatively high cost of navigational or tactical grades of inertial measurement units (IMUs) needed to obtain reliable independent positioning and navigation during GNSS outages. Low cost, small, lightweight and low power consumption Micro-Electro-Mechanical Systems (MEMS)-based inertial sensors may be used together with low cost GNSS receivers, but the performance of the navigation system will degrade very quickly in contrast to the higher grade IMUs in areas with little or no GNSS signal availability due to time-dependent accumulation of errors from the INS.
Speed information from the odometric readings, or from any other source, may be used to enhance the performance of the MEMS-based integrated INS/GNSS solution by providing velocity updates, however, current INS/Odometry/GNSS systems continue to be plagued with the unbounded growth of errors over time during GNSS outages.
One reason for the continued problems is that commercially available navigation systems using INS/GNSS integration or INS/Odometry/GNSS integration rely on the use of traditional Kalman Filter (KF)-based techniques for sensor fusion and state estimation. The KF is an estimation tool that provides a sequential recursive algorithm for the estimation of the state of a system when the system model is linear.
As is known, the KF estimates the system state at some time point and then obtains observation “updates” in the form of noisy measurements. As such, the equations for the KF fall into two groups:                Time update or “prediction” equations: used to project forward in time the current state and error covariance estimates to obtain an a priori estimate for the next step, or        Measurement update or “correction” equations: used to incorporate a new measurement into the a priori estimate to obtain an improved posteriori estimate.        
While the commonly used Linearalized KF (LKF) and Extended KF (EKF) can provide adequate solutions when higher grade IMUs are utilized by linearizing the originally nonlinear models, the KF generally suffers from a number of major drawbacks that become influential when using low cost MEMS-based inertial sensors, as outlined below.
The INS/GNSS integration problem at hand has nonlinear models. Thus, in order to utilize the linear KF estimation techniques in this type of problem, the nonlinear INS/GNSS model has to be linearized around a nominal trajectory. This linearization means that the original (nonlinear) problem be transformed into an approximated problem that may be solved optimally, rather than approximating the solution to the correct problem. The accuracy of the resulting solution can thus be reduced due to the impact of neglected nonlinear and higher order terms. These neglected higher order terms are more influential and cause error growth in the positioning solution, in degraded and GNSS-denied environments, particularly when low cost MEMS-based IMUs are used.
Further, the KF requires an accurate stochastic model of each of the inertial sensor errors, which can be difficult to obtain, particularly where low cost MEMS-based sensors are used because they suffer from complex stochastic error characteristics. The KF is restricted to use only linear low-order (low memory length) models for these sensors' stochastic errors such as, for example, random walk, Gauss-Markov models, first order Auto-Regressive models or second order Auto-Regressive models. The dependence of the KF on these inadequate models is also a drawback of the KF when using low cost MEMS-based inertial sensors.
As a result of these shortcomings, the KF can suffer from significant drift or divergence during long periods of GNSS signal outages, especially where low cost sensors are used. During these periods, the KF operates in prediction mode where errors in previous predictions, which are due to the stochastic drifts of the inertial sensor readings not well compensated by linear low memory length sensors' error models and inadequate linearized models, are propagated to the current estimate and summed with new errors to create an even larger error. This propagation of errors causes the solution to drift more with time, which in turn causes the linearization effect to worsen because of the drifting solution used as the nominal trajectory for linearization (in both LKF and EKF cases). Thus, the KF techniques suffer from divergence during outages due to approximations during the linearization process and system mis-modeling, which are influential when using MEMS-based sensors.
In addition, the traditional INS typically relies on a full inertial measurement unit (IMU) having three orthogonal accelerometers and three orthogonal gyroscopes. This full IMU setting has several sources of error, which, in the case of low-cost MEMS-based IMUs, will cause severe effects on the positioning performance. The residual uncompensated sensor errors, even after KF compensation, can cause position error composed of three additive quantities: (i) proportional to the cube of GNSS outage duration and the uncompensated horizontal gyroscope biases; (ii) proportional to the square of GNSS outage duration and the three accelerometers uncompensated biases, and (iii) proportional to the square of GNSS outage duration, the horizontal speed, and the vertical gyroscope uncompensated bias.
Another traditional solution, known as Dead reckoning, which can be used to provide a two dimensional (2D) positioning solution for land vehicles using a single axis gyroscope vertically aligned with the vehicle and the speed readings from an odometer. Dead reckoning relies on an assumption that vehicles will primarily move on the horizontal plane. However, this solution is also plagued with certain drawbacks, namely: (i) it is a 2D solution that does not estimate the altitude nor the vertical component of velocity; and (ii) assuming that the vehicle is moving in the horizontal plane, it disregards the tilt angles of the vehicles and subsequently the off-plane motion which causes two main issues: (a) the assumption that the gyroscope vertically aligned to the vehicle also has its axis in the pure vertical (i.e. normal to the East-North plane), which is a problem because its axis is actually tilted, will affect the accuracy of the azimuth calculation, and (b) the assumption that the vehicle's traveled path is horizontal, which is a problem because the vehicle and its path are actually tilted, will cause an error in the horizontal position estimation.
The foregoing drawbacks of the KF have resulted in increased investigation into alternative methods of INS/GNSS integration models, such as, for example, nonlinear artificial intelligence techniques. However, there is a need for enhancing the performance of low-end systems relying on low cost MEMS-based INS/GNSS sensors and for mitigating the effect of all sources of errors to provide a more adequate navigation solution. Further, there is also a need for more advanced modeling techniques that are capable of modeling the stochastic sensor errors instead of the linear low memory length models currently used.